To factor out the expression \((x + 2)(x + 1)\), we will use the distributive property (also known as FOIL for binomials). Here's the step-by-step process:

\[
(x + 2)(x + 1) = x(x + 1) + 2(x + 1)
\]

Now distribute each term:

\[
= x^2 + x + 2x + 2
\]

Combine like terms:

\[
= x^2 + 3x + 2
\]

Thus, the expanded form of \((x + 2)(x + 1)\) is \(x^2 + 3x + 2\).

Do you have any questions or want further details?

Here are five related questions to further your understanding:
1. How would you factor \(x^2 + 3x + 2\) back into binomials?
2. What is the difference between expanding and factoring?
3. Can you apply the FOIL method to factor trinomial expressions like \(x^2 + 3x + 2\)?
4. How does factoring differ when dealing with negative coefficients?
5. How does factoring help in solving quadratic equations?

**Tip:** Always check your factored or expanded form by multiplying it out again to verify its correctness.

Learn how to expand and factor the binomial expression (x+2)(x+1) step by step using the distributive property. This problem covers key algebraic concepts, including the FOIL method and combining like terms. Suitable for students in Grades 8-10.

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